Abstract: The suppliers often provide the trade credit for the payment of the amount owed. Usually, there is no interest charged for the retailer if the outstanding amount is paid in the allowable delay. If the payment is unpaid in full by the end of the permissible delay period, interest is charged on the outstanding amount. The inventory replenishment policies under trade credit financing have been studied intensively. But most of the existing inventory models under trade credit financing are assumed that a constant demand and the infinite or a constant replenishment rate. However, in practice, the demand rate is the ramp type function of time for some cases, such as the new products and the holiday related products. On the other hand, the production rate is related to the market demand. Therefore, the optimal order strategy of the retailer was discussed based on the trade credit financing, considering the time varying supply and demand. First, according to the relationship of the trade credit period and the retailer's replenishment cycle, the retailer's inventory models are constructed from two kinds of situations; Second, based on the inventory model, the existence of the optimal solutions is proved and give related theorems and the algorithms are given to solve the retailer's optimal inventory strategy; Finally, the numerical example and sensitivity analysis are carried out to demonstrate the related conclusions. The results show that: when the supplier gives the retailer's short trade credit period, which is less than the stable point of the demand, with the increase of stable point time, the retailer's optimal order cycle, the optimal order quantity and the annual cost decreases; when the supplier gives the retailer's trade credit period long, greater than the stable point of the demand, with the increase of stable point time, the retailer's optimal order cycle, the optimal order quantity and the annual cost also increases; with the dependence of suppliers' production on the demand stronger, the retailer's optimal order cycle, the optimal order quantity and the annual cost also increases. The paper extends the EOQ models and enables the managers to make the replenishment policies more effectively.

Key words: trade credit financing, the ramp type demand, replenishment time dependent on the demand, order policy